M3381251 Mersenne number exponent details

Residue

Status

L-L

F0371D71880B37CA

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	17.6281	67.6471%	1127083	111642300	1.0886	7.5687%	18.7167	70.0958%	2.4487%
PrimeNet	2⁶⁰	0.0454	63.3333%	14000	280000	0.0043	2.8444%	0.0498	64.3763%	1.0429%
GPU72	2⁶⁴	1.0527	65.6250%	18000	320000	0.0052	1.7902%	1.0579	66.2404%	0.6154%
Difference	+4	+16.5754	+2.0221%	+1109083	+111322300	+1.0834	+5.7785%	+17.6588	+3.8554%	+3.8554%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.6281

67.6471%

1127083

111642300

1.0886

7.5687%

18.7167

70.0958%

2.4487%

PrimeNet

2⁶⁰

0.0454

63.3333%

14000

280000

0.0043

2.8444%

0.0498

64.3763%

1.0429%

GPU72

2⁶⁴

1.0527

65.6250%

18000

320000

0.0052

1.7902%

1.0579

66.2404%

0.6154%

Difference

+16.5754

+2.0221%

+1109083

+111322300

+1.0834

+5.7785%

+17.6588

+3.8554%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3381251	13012535728324526423	20	63.497	1924219131961 7 × 9733 × 28242931	2014-10-24	9733	28242931	0.8266	0.2357	0.4377

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3381251

13012535728324526423

63.497

1924219131961
7 × 9733 × 28242931

2014-10-24

9733

28242931

0.8266

0.2357

0.4377

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T19:18:00	Carsten Kossendey	durandal	15000	206250		-		-	-	0.004	-	-	0.811%
2011-10-20T14:16:00	harlee	P4_2600	60000	930000		-		-	-	0.016	-	-	1.881%
2014-06-26T02:26:00	ANONYMOUS	Manual testing	78982	78982		-		-	-	0.012	-	-	0.755%
2014-10-12T23:58:00	Jocelyn Larouche	Manual testing	97964	97964		-		-	-	0.015	-	-	0.860%
2021-03-13T12:05:35	Jocelyn Larouche	Manual testing	338125	3719376	6	-		-	-	0.080	-	-	3.536%
2022-01-09T11:51:32	Jocelyn Larouche	Manual testing	1127083	111642300		-	skipped known factor: 13012535728324526423	-	-	1.089	-	-	7.569%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-26T05:53:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.045	-	-
2011-08-25T21:18:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.091	-	-
2022-04-24T06:27:37	LordJulius	Manual testing	2¹	2⁶²		-	-	0.182	-	-
2012-11-15T00:22:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.472	-	-
2022-04-24T06:27:37	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.290	-	-
2022-04-24T06:27:37	LordJulius	Manual testing	2⁶³	2⁶⁴	13012535728324526423	63.497	20	0.355	0.721	0.720
2022-04-24T06:27:37	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.105	-	-
2022-04-24T06:27:37	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.210	-	-
2022-04-24T06:27:37	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.420	-	-
2021-07-01T05:54:09	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.840	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.318 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.318 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.879
50000	5000000	13012535728324526423	3	0.439

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-20T06:29:00	mdrg	MDRG02	50000	5000000						3	0.439
2011-12-14T00:52:00	Smurgs	Praca	50000	5000000						3	0.439
2014-10-24T01:24:00	Sid & Andy	Mrs_Potato_Head	50000	5000000	13012535728324526423	63.497	3	2		3	0.439

date	userid	compid	res64	spent (GHz-days)
1999-09-30T00:00:00	ANONYMOUS	v4_computers	F0371D71880B37CA	0.355

date

userid

compid

res64

spent (GHz-days)

1999-09-30T00:00:00

ANONYMOUS

v4_computers

F0371D71880B37CA

0.355

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-05T07:41:44

kkmrkkblmbrbk

c4.xlarge

13012535728324526423

A361B0CED4E880__

2017-11-20T23:07:54

Oliver Kruse

GTX-3

13012535728324526423

A361B0CED4E880__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1127083, B2 = 111642300 (P-1 stage 2)

B1 = 1127083 (P-1 stage 1)

B1 = 338125, B2 = 3719376 (P-1 stage 2)

B1 = 338125 (P-1 stage 1)

B1 = 60000, B2 = 930000 (P-1 stage 2)

B1 = 97964 (P-1 stage 1)

B1 = 78982 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 206250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront